
theorem Th86:
  for F being non empty Graph-yielding Function, x being Element of dom F
  for x9 being Element of dom canGFDistinction F st x = x9
  holds (canGFDistinction F).x9 is F.x-Disomorphic
proof
  let F be non empty Graph-yielding Function, x be Element of dom F;
  let x9 be Element of dom canGFDistinction F;
  assume x = x9;
  then consider G being PGraphMapping of F.x,(canGFDistinction F).x9 such that
    G_V = renameElementsDistinctlyFunc(the_Vertices_of F,x) &
    G_E = renameElementsDistinctlyFunc(the_Edges_of F,x) and
    A1: G is Disomorphism by Th85;
  thus thesis by A1, GLIB_010:def 24;
end;
